The head of Saxony's state government, Michael Kretschmer, said his conservative CDU party was capable of remaining in power.
Exit polls from Sunday's elections give his party a thin lead over the far-right AfD.
The CDU has excluded building a coalition with the AfD. Without an absolute majority, the CDU will be forced to look for coalition partners among the remaining parties in the state parliament, including the BSW, the Greens, and the SPD.
Kretschmer said the "coalition accord would be made for the state and for the people."
"It won't be easy," he said.
"But one thing is certain: with many discussions and the will to do something for this state, we can succeed in using this election result to give Saxony a stable government that serves the state and leads the way with humility," he added.